The most knowledgeable people are always those who are not responsible. Either they don't know anything but are skilled at ducking out or they know enough to stay away from that particular responsibility.

Domain Name Service (DNS) has been suspended from the domain because of overdue payment.
wakeofgods.org domain has been using DNSEver service since 10 05, 2014.
DNSEver provides the Domain Name Service (DNS) to connect the domain and the server IP.

I click on their payment option, kaspersky says phising action and blocks the site. I try to register at dnsever, I receive confirmation email (which I must click to register):

DNS service asks me to pay 0,42 $$/month. But I can't even pay, their automatic pay options start at 40$ and to enter custom price (1$ in this case) you need to be registered. Or their confirmation email has unknown code to me. Beside, my antivirus warns me about their site and constantly blocks it.

As we see, things changed on 10/05/2014, when DNS entered in the game. When I bought domain, there was no dns.

Your domain is not suspended. Every service we provide is working correctly. You are just using a third party name servers and they have suspended your service for it. I do not know who told you to set them up like this. We can provide you with the information on how to solve the issue if you are willing to work with us.

It was you who choose dns service? because I never set anything. Let's solve this.

I have no idea where you got those nameservers, but they are clearly a scam. So why did you enter them in the first place when you register your domain. You can log into your client area https://manage.host1plus.com/clientarea.php , select "my domains", click edit near the domain, then you will be able to register your own nameservers. There is a button below "Register name servers" click it. Then create ns1.domain.tld and ns2.domain.tld pointing to your VPS. You will have to install bind or similar service on your VPS.